Related papers: Geometric phase in the G3+ quantum state evolution
It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems.…
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…
We discuss the presence of a geometrical phase in the evolution of a qubit state and its gauge structure. The time evolution operator is found to be the free energy operator, rather than the Hamiltonian operator.
Geometric phases, which accompany the evolution of a quantum system and depend only on its trajectory in state space, are commonly studied in two-level systems. Here, however, we study the adiabatic geometric phase in a weakly anharmonic…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state…
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use…
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…